Calculating the shortest distance between polygons in QGIS

Question

In QGIS 3.12 I need to calculate the shortest distance from the boundary of one polygon to the boundary lines of a set of polygons as shown in the image below

I have followed the instructions according to this question Calculating shortest distance between multiple Polygon borders to a common Polygon border?.

It seemed to provide a good solution using the field calculator to generate a new feature in the attribute table (eg the attribute table of the blue polygons) using the following formula

distance($geometry, geom_from_wkt('Polygon ((........))'))

as described in the above link. However, when I randomly checked some of the distances using the measuring tool, while many of my tests were consistent, I found several that were incorrect e.g 196.11 km vs 216.9 km.

All the shapefiles and my project are in the same projection system.

I cannot figure out why there are the errors or if this is the best way to calculate these distances.

Ideally I would like tracklines generated to show the shortest distance, however this may be over complicated.

Answer 1

If only length values are needed, please use the following expression in the "Field Calculator"

length(
    shortest_line(
        $geometry,
        geometry(get_feature('building', 'osm_id', '1234567'))
        )
    )

In my example I am referring to a feature by its "id" from a certain layer, otherwise use geom_from_wkt().

If new geometries have to be created, then try using the "Geometry by expression" geoalgorithm from the QGIS's Processing Toolbox (Ctrl+Alt+T) with the following expression:

shortest_line(
    $geometry,
    geometry(get_feature('building', 'osm_id', '1234567'))
    )